[1701.07592] Smooth structures on $\mathbb{C}P^{m}$ for $5\leq m\leq 8$ Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Geometric Topology arXiv:1701.07592 (math) This paper has been withdrawn by Ramesh Kasilingam [Submitted on 26 Jan 2017 ( v1 ), last revised 1 May 2026 (this version, v4)] Title: Smooth structures on $\mathbb{C}P^{m}$ for $5\leq m\leq 8$ Authors: Ramesh Kasilingam View a PDF of the paper titled Smooth structures on $\mathbb{C}P^{m}$ for $5\leq m\leq 8$, by Ramesh Kasilingam No PDF available, click to view other formats Abstract: We classify up to diffeomorphism all smooth manifolds homeomorphic to the complex projective m-space $\mathbb{C}P^{m}$ for $m = 5, 6, 7$ and $8$. As an application, for $m = 7$ and $8$, we compute the smooth tangential structure set of $\mathbb{C}P^{m}$ and obtain a bound on the number of smooth homotopy complex projective m-spaces with given Pontryagin classes up to orientation-preserving diffeomorphism. We also show that there exists a smooth manifold which is tangentially homotopy equivalent but not homeomorphic to $\mathbb{C}P^{8}$. Comments: This manuscript has been substantially revised, resulting in a new version with largely non-overlapping text, although it addresses the same research problem. The revised paper has been submitted separately and is available under the arXiv ID: 2604.27521 . In light of this, I kindly ask for your approval to withdraw the earlier version Subjects: Geometric Topology (math.GT) MSC classes: 57R55, 55P42, 57R60, 57R67 Cite as: arXiv:1701.07592 [math.GT] (or arXiv:1701.07592v4 [math.GT] for this version) https://doi.org/10.48550/arXiv.1701.07592 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Ramesh Kasilingam [ view email ] [v1] Thu, 26 Jan 2017 07:04:14 UTC (10 KB) [v2] Mon, 1 Jan 2018 14:59:15 UTC (10 KB) [v3] Mon, 6 Feb 2023 11:50:54 UTC (16 KB) [v4] Fri, 1 May 2026 03:37:15 UTC (1 KB) (withdrawn) Full-text links: Access Paper: View a PDF of the paper titled Smooth structures on $\mathbb{C}P^{m}$ for $5\leq m\leq 8$, by Ramesh Kasilingam Withdrawn No license for this version due to withdrawn Current browse context: math.GT < prev | next > new | recent | 2017-01 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from